1

I have found a similar question at Calculate Rotation Matrix to align k n dimensional vectors but not quite the same what I want to do.

Problem:

$S_1, S_2 \in \Re^{D \times d} $ where ${D > d} $ and columns of each matrix are orthonormal. Need to find a $R \in \Re^{D \times D}$ orthonormal rotation matrix such that $Col(S_2) \equiv Col(R S_1)$ where $Col(\cdot)$ represents the column space.

Any insight towards a solution is much appreciated.

Batta
  • 173

1 Answers1

0

Found a solution based on the answer at rotating linear dependent vectors in space.

In our case $S_1$ and $S_2$ are each similar to $A$ matrix described in above answer. For $S_1$ and $S_2$, find corresponding $G$ matrices $G_1$ and $G_2$. Finally the needed rotation $R=G_2 G_1^{-1}$.

Batta
  • 173